# KarhunenLoeveReduction¶

class KarhunenLoeveReduction(*args)

Perform the reduction of a field.

This object projects a field on the Karhunen-Loeve basis by computing the coefficients, lifts the coefficients, combines them with the value of the modes on the mesh which creates the reduced field.

Parameters
resultKarhunenLoeveResult

Decomposition result.

trendTrendTransform, optional

Process trend, useful when the basis built using the covariance function from the space of trajectories is not well suited to approximate the mean function of the underlying process.

Examples

Create a KL decomposition of a Gaussian process:

>>> import openturns as ot
>>> numberOfVertices = 10
>>> interval = ot.Interval(-1.0, 1.0)
>>> mesh = ot.IntervalMesher([numberOfVertices - 1]).build(interval)
>>> covariance = ot.SquaredExponential()
>>> process = ot.GaussianProcess(covariance, mesh)
>>> sampleSize = 10
>>> sample = process.getSample(sampleSize)
>>> threshold = 0.0
>>> algo = ot.KarhunenLoeveSVDAlgorithm(sample, threshold)
>>> algo.run()
>>> klresult = algo.getResult()


Generate some trajectories and reduce them:

>>> sample2 = process.getSample(5)
>>> reduction = ot.KarhunenLoeveReduction(klresult)
>>> reduced = reduction(sample2)


Same, but into account the trend:

>>> trend = ot.TrendTransform(ot.P1LagrangeEvaluation(sample.computeMean()), mesh)
>>> reduction = ot.KarhunenLoeveReduction(klresult, trend)
>>> reduced = reduction(sample2)


Methods

 __call__(*args) Call self as a function. Get the number of calls of the function. Accessor to the object’s name. Accessor to the object’s id. Get the description of the input field values. Get the dimension of the input field values. Get the mesh associated to the input domain. getMarginal(*args) Get the marginal(s) at given indice(s). Accessor to the object’s name. Get the description of the output field values. Get the dimension of the output field values. Get the mesh associated to the output domain. Accessor to the object’s shadowed id. Accessor to the object’s visibility state. Test if the object is named. Test if the object has a distinguishable name. Whether the function acts point-wise. setInputDescription(inputDescription) Set the description of the input field values. setInputMesh(inputMesh) Set the mesh associated to the input domain. setName(name) Accessor to the object’s name. setOutputDescription(outputDescription) Set the description of the output field values. setOutputMesh(outputMesh) Set the mesh associated to the output domain. Accessor to the object’s shadowed id. setTrend(trend) Trend accessor. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

getCallsNumber()

Get the number of calls of the function.

Returns
callsNumberint

Counts the number of times the function has been called since its creation.

getClassName()

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getInputDescription()

Get the description of the input field values.

Returns
inputDescriptionDescription

Description of the input field values.

getInputDimension()

Get the dimension of the input field values.

Returns
dint

Dimension of the input field values.

getInputMesh()

Get the mesh associated to the input domain.

Returns
inputMeshMesh

The input mesh .

getMarginal(*args)

Get the marginal(s) at given indice(s).

Parameters
iint or list of ints,

Indice(s) of the marginal(s) to be extracted.

Returns
fieldFunctionFieldFunction

The initial function restricted to the concerned marginal(s) at the indice(s) .

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOutputDescription()

Get the description of the output field values.

Returns
outputDescriptionDescription

Description of the output field values.

getOutputDimension()

Get the dimension of the output field values.

Returns
d’int

Dimension of the output field values.

getOutputMesh()

Get the mesh associated to the output domain.

Returns
outputMeshMesh

The output mesh .

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

isActingPointwise()

Whether the function acts point-wise.

Returns
pointWisebool

Returns true if the function evaluation at each vertex depends only on the vertex or the value at the vertex.

setInputDescription(inputDescription)

Set the description of the input field values.

Parameters
inputDescriptionsequence of str

Description of the input field values.

setInputMesh(inputMesh)

Set the mesh associated to the input domain.

Parameters
inputMeshMesh

The input mesh .

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setOutputDescription(outputDescription)

Set the description of the output field values.

Parameters
outputDescriptionsequence of str

Describes the outputs of the output field values.

setOutputMesh(outputMesh)

Set the mesh associated to the output domain.

Parameters
outputMeshMesh

The output mesh .

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setTrend(trend)

Trend accessor.

Parameters
trendTrendTransform, optional

Process trend, useful when the basis built using the covariance function from the space of trajectories is not well suited to approximate the mean function of the underlying process.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.